Coin Picking

Question:

There is a large* pile of coins in a room. Almost all of them are turned heads up,
except just 20 which are turned tails up. You know this, but are wearing a blindfold
and gloves (which cannot be removed) so you have no way of telling which are heads
and which are tails.

The challenge: split the coins into two groups, such that both groups have the same number
of coins which are tails up. How would you achieve this?

*it can be assumed that there are infinitely many coins.

Hint: the piles do not have to be the same size, which makes sense as the original pile is endless!

Take any 20 coins from the pile and turn them all over to the opposite face. Now you have
completed the challenge!

This works because:
Of the 20 coins you chose, x are tails, where x is between 0 and 20. In the large
pile there were originally 20 tails, but now there are 20-x tails. You've taken 20-x
heads from the large pile, and turned them over to be tails.

So now there are 20-x tails up coins in each pile!

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